The problem in Eq. (REF ) is optimized based on majorization-minimization [1]} and proximal-averaging [2]}. The update \(x\)  at \((k+1)^{\text{th}}\)  iteration is obtained by solving the following optimization problem:
\(\underset{x}{\min } ~\frac{1}{2\rho }\Vert x - r^{(k+1)}\Vert ^2_2 + \sum _{i=1}^{p} \alpha _i g_i(\mathcal {F}(x)),\) 
